On association models defined over independence graphs

Bernoulli

Volumn 4, Issue 4, 1998, Pages 477-495

  Wermuth, Nanny ^a   Cox, David R ^b  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b NUFFIELD COLLEGE   (United Kingdom)

Author keywords

conditional independence; graphical Markov model; quasi linear dependence; separation criteria; triangular matrix decomposition

Indexed keywords

EID: 0000316899     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318662     Document Type: Article

References (31)

1. Anderson, T.W. (1984) Introduction to Multivariate Statistical Analysis, 2nd edn. New York: Wiley.
2. Bolviken, E. (1982) Probability inequalities for the multivariate normal with nonnegative partial correlations. Scand. J. Statist., 9, 49-58.
3. Cochran, W.G. (1938) The omission or addition of an independent variate in multiple linear regression. J. Roy. Statist. Soc., Suppl., 5, 171-176.
4. Cox, D.R. and Wermuth, N. (1992) Response models for mixed binary and quantitative variables. Biometrika, 79, 441-461.
5. Cox, D.R. and Wermuth, N. (1993) Linear dependencies represented by chain graphs (with discussion). Statist. Sci., 8, 204-218; 247-277.
6. Cox, D.R. and Wermuth, N. (1994) A note on the binary quadratic exponential distribution. Biometrika, 81, 403-408.
7. Cox, D.R. and Wermuth, N. (1996) Multivariate Dependencies-Models, Analysis and Interpretation. London: Chapman & Hall.
8. Darroch, J.N., Lauritzen, S.L. and Speed, T.P. (1980) Markov fields and log-linear models for contingency tables. Ann. Statist., 8, 522-539.
9. Dempster, A.P. (1969) Elements of Continuous Multivariate Analysis. Reading, Massachusetts: Addison-Wesley.
10. Edwards, D. (1995) Introduction to Graphical Modelling. New York: Springer-Verlag.
11. Frydenberg, M. (1990) The chain graph Markov property. Scand. J. Statist., 17, 333-353.
12. Karlin, S. and Rinott, Y. (1983) M-matrices as covariance matrices of multinormal distributions. Linear Algebra Applic., 52-53, 419-438.
13. Kauermann, G. (1996) On a dualization of graphical Gaussian models. Scand J. Statist., 23, 105-116.
14. Kiiveri, H.T., Speed, T.P. and Carlin, J.B. (1984) Recursive causal models. J. Austral. Math. Soc. A, 36, 30-52.
15. Lauritzen, S.L. (1996) Graphical Models. Oxford: Oxford University Press.
16. Lauritzen, S.L., Dawid, A.P., Larsen, B. and Leimer, H.-G. (1990) Independence properties of directed Markov fields. Networks, 20, 491-505.
17. Lauritzen, S.L. and Wermuth, N. (1989) Graphical models for associations between variables, some of which are qualitative and some quantitative. Ann. Statist., 17, 31-57.
18. Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, California: Morgan Kaufmann.
19. Pearl, J. and Verma, T. (1988) The logic of representing dependencies by directed graphs. Proceedings of the American Association of Artificial Intelligence Conference, Seattle, Washington.
20. Pearl, J. and Wermuth, N. (1994) When can association graphs admit a causal interpretation? In P. Cheseman and W. Oldford (eds), Models and Data, Artificial Intelligence and Statistics IV, pp. 205-214. New York: Springer-Verlag.
21. Spirtes, P., Glymour, C. and Scheines, R. (1993) Causation, Prediction and Search. New York: Springer-Verlag.
22. Wermuth, N. (1976) Analogies between multiplicative models for contingency tables and covariance selection. Biometrics, 32, 95-108.
23. Wermuth, N. (1980) Linear recursive equations, covariance selection, and path analysis. J. Amer. Statist. Assoc., 75, 963-997.
24. Wermuth, N. (1989) Moderating effects in multivariate normal distributions. Methodika, 3, 74-93.
25. Wermuth, N. (1992) On block-recursive linear regression equations (with discussion). REPRABE (Brazilian J. Probab. Statist.), 6, 1-56.
26. Wermuth, N. (1995) On the interpretation of chain graphs. Proceedings of the 50th Session of International Statistical Institute, Beijing 1995, Book 1, pp. 415-429.
27. Wermuth, N. (1997) Graphical Markov models. In S. Kotz, C. Read and D. Banks (eds), Encyclopedia of Statistical Sciences. New York: Wiley. To appear.
28. Wermuth, N. and Cox, D.R. (1998) Statistical dependence and independence. In P. Armitage and T. Colton (eds), Encyclopedia of Biostatistics. New York: Wiley. To appear.
29. Wermuth, N. and Lauritzen, S.L. (1983) Graphical and recursive models for contingency tables. Biometrika, 70, 537-552.
30. Wermuth, N. and Lauritzen, S.L. (1990) On substantive research hypotheses, conditional independence graphs and graphical chain models (with discussion). J. Roy. Statist. Soc. B, 52, 21-72.
31. Wright, S. (1923) The theory of path coefficients: a reply to Niles' criticism. Genetics, 8, 239-255.